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Magnetic ordering in TbRh2Si2 and CeRh2Si2
1038-1098/84 $3.00 + .00 Pergamon Press Ltd.
Solid State Communications, Vol. 49, No. 7, pp. 685-691, 1984. Printed in Great Britain. MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2 S. Quezel, J. Rossat-Mignod
Laboratoire de Diffraction Neutronique, D6partement de Recherche Fondamentale, Centre d'Etudes Nucl6aires, 85X-38041 Grenoble C6dex, France and B. Chevalier, P. Lejay, J. Etourneau Laboratoire de Chimie du Solide du CNRS, Universit6 de Bordeaux I, 351, cours de la Lib6ration - 33405 Talence C6dex, France
(Received 28 October 1983 by E. F. Bertaut) Magnetic measurements and a neutron diffraction study have been carried out on the ternary compounds TbRh2Si2 and CeRh2Si2 with a tetragonal structure of ThCr2Si2-type. TbRh2Si2 is found to order antiferromagnetically below TN = 92 K with moments along the e-axis. The structure, of wave vector k = [001 ], consists of a stacking of ferromagnetic (001) planes with a + -- + - - sequence. CeRh2Si2 develops below TN = 36 K a structure described by a wave vector k = [1/2 1/2 0] in which the coupling within a (001) plane is antiferromagnetic. This change of coupling together with the large negative value of0p = - 61 K has been attributed to a change of the sign of the first nearest neighbour in-plane interaction which would correspond to an exchange mechanism different from the usual RKKY one in CeRh2Si2. 1. INTRODUCTION THE TERNARY SILICIDES RM2Si2 in which R is a rare earth metal and M is a 3d, 4d or 5d transition element have been extensively studied during the past years. They crystallize in a simple structure of ThCr2Si~type which is tetragonal of space group I4/mmm [1 ]. These ternary silicides allow us to study many interesting physical properties as the supraconductivity, the valence fluctuations, the Kondo effect or the magnetism [2-4]. The magnetic properties of the silieides with a 3d transition element (Mn, Fe, Co, Ni, Cu) have been studied in more detail than those with a noble metal as M = Ru, Rh, Ir. In a recent work we have shown that the RRh2Si 2 (R = Ce, Nd, Sm, Gd, Tb, Dy, Ho, Er) exhibit at low temperatures an antiferromagnetic ordering [2]. In this paper we report the results of a more detailed study on the CeRh2Si2 and TbRh2Si2 silicides by means of neutron diffraction and magnetic measurements.
1.1. Sample preparation CeRh2Si2 and TbRh2Si2 have been prepared by the direct melting of the elements in an arc furnace under a purified argon atmosphere. The obtained compounds were analyzed by X-rays using a Guinier camera and proved to have the quadratic structure of ThCr2Si2type. The lattice parameters at room temperature of
CeRh:Si2 (a = 4.075 A, c = 10.13 A) and of TbRh2Si2 (a = 4.031 A, c = 9.96 A) are in good agreement with the previously published values [5]. In the case of TbRh2Si2 a single crystal (3 mm diameter and 2 mm height) has been grown by using a Czochralski method developed at the University of Bordeaux [6]. 2. MAGNETIC MEASUREMENTS The magnetic measurements have been performed between 4.2 K and 300 K by using a balance of Faraday type and a magnetometer with a vibrating sample. CeRh2Si2 orders antiferromagnetically at TN = 36 K. The magnetic susceptibility follows a Curie-Weiss law (Fig. 1). The effective moment value/ae~ ~ = 2.56/a B is in agreement with cerium in a trivalent state. The paramagnetic Curie temperature 0p = --61 K has a large negative value. These values differ significantly from the quite recent measurements of Godart et al. (0p = -- 72 K, ~ten = 2.9/aB) [7]. TbRh2Si2 orders also antiferromagnetically at TN = 94K. The effective moment value/aen = 10.0/l n is slightly larger than the free ion value of a Tb 3+ ion (/aen = 9.72/~B) which may indicate a positive polarization of the conduction electrons. The paramagnetic Curie temperature 0p = 43 K has a positive value, as in most of the other RRh2Si2 ternaries [2], indicating that 685
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MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
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TEMPERATURE
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Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility of CeRh2Si2.
(K)
Fig. 3. Temperature dependence of the magnetization of a TbRh2Si2 single crystal measured with a magnetic field of 18 kOe applied along and perpendicularly to the c-axis. the interactions have mainly a ferromagnetic character in TbRh2Si2 (Fig. 2). The magnetization measured on a single crystal, exhibits a large anisotropy depending on the magnetic field is applied along or perpendicularly to the c-axis (Fig. 3). The antiferromagnetic direction is along the c-axis. 3. NEUTRON RESULTS
/ 20
Tb Rh2Si 2
Neutron experiments have been carried out at the Siloe reactor of the CEN-Grenoble. The diffraction patterns were recorded with a linear multidetector spectrometer [8] using a neutron wavelength of 2.483 A. The scattering by the nucleus gives rise to nuclear Bragg peaks which can be well accounted by the extinction condition (h + k + l = 2n + 1) of the body centered-tetragonal space group I4/mmm. The crystal structure of ThCr2Si2-type contains:
/
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1,5 O
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one R atom in the site 2a: (000) of D4h symmetry; two Rh atoms in the site 4d: (0½¼) and (½0¼); two Si atoms in the site 4e: (00z) and (00~).
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I'EMPERAIURE {K)
Fig. 2. Temperature dependence of the reciprocal magnetic susceptibility of TbRh2Si2.
Then the structure can be described as a stacking of atomic planes perpendicular to the c-axis with the sequence R - S i - R h - S i - R and located respectively at z = 0, 1/2 --Zsi = 0.125, 1/4, Zsi = 0.375 and 1/2. The fit of the calculated and integrated intensities gives no evidence for any mixing between Rh and Si atoms in 4d and 4e sites. As an example a comparison between observed and calculated intensities of a few nuclear peaks are given in Table 1 in the case of TbRh2Si2. A quite good agreement (R = 2.7%) is obtained for Zsi = 0.375, the intensities were calculated using
Vol. 49, No. 7
MAGNETIC ORDERING IN TbRh2Siz AND CeRh=Si2
Tb Rh2Si 2
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BRAGG ANGLE (0) Fig. 4. (a) Neutron diffraction patterns from paramagnetic (103 K) and ordered (15 K) TURh2Si~. Magnetic reflections are associated with a wave vector k = [001 ]. (b) Neutron diffraction patterns from paramagnetic (106 K) and ordered (10 K) CeRh2Si2. Magnetic reflections are associated with a wave vector k = [1/2 1/2 0]. the following scattering lengths: ban, = 0.756, bah = 0.591, bsi = 0.415 x 10-12 cm. As far as the magnetic properties are concerned this structure is quite simple because the magnetic ions (rare earth) are located in one Bravais lattice.
TbRhaSi2 In the neutron diffraction diagrams given in Fig. 4 additional reflections can be identified at T = 15 K. These new reflections, due to the onset of the magnetic order, can be easily indexed on the basis of the
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MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2 C e Rh 2 5i
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Vol. 49, No. 7
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Table 2. Calculated and observed intensities o f the magnetic superlattice peaks o f TbRh2Si2 in barn/Tb atom at T = 15K. hk l
lob s
001 1 00 003 1 02 111 1 13 1 04 005 20 1
n.0 17.2 n.0 18.7 29.5 12.4 6.0 n.0 22.1 mo=8.5-+0.3/aB
I~ 0 17.8 0 18.6 26.5 13.1 6.1 0 19.7 R=6.5%
crystallographic unit cell with the following rule h + k + l = 2n 4- I. The magnetic scattering vectors h being defined by the relation h = H + k, whre H spanned the different Brillouin zone centers i.e. the nuclear
Fig. 6. (a) Temperature dependence of the magnetic intensity of the [100] reflection of TbRh2Si 2. (b) Temperature dependence of the integrated intensity of the [1/2 1/2 0] magnetic reflection of CeRh2Si2. lattice vectors, the ordering is described by the wave vector k = [001 ]. This wave vector corresponds to a symmetry point of the Brillouin zone (for c > a) i.e. it describes a truly antiferromagnetic structure [9]. The structure consists of a stacking of ferromagnetic (001) planes with a + - - + - - sequence along the c-axis (Fig. 5). The absence of the [001 ], [0 03] magnetic peaks indicates without any ambiguity that the moments are aligned along the e-axis. The observed intensities (Table 2) can be well accounted (R = 6.7%) by using the Tb 3÷ form factor given by [10]. A moment value mo = 8.5 -+ 0.3/a n is found at T = 15 K indicating that the terbium magnetic moment is close to the free ion value ( g J = 9/an). Moreover there is no evidence of any magnetic moment on the rhodium atoms. The temperature dependence of the [100] magnetic
Vol. 49, No. 7
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
Table 3 Calculated and observed intensities of the magnetic superlattice peaks of CeRh~Si2 in barn/Ce atom at T = 10 K. Magnetic peaks are indexed in the domain associated with k~ = [1/2 1/2 0]. h kl
Iobs
Ieaa
~½0 "I" I ~ 1 ½½2 ½½3 ~0 ~1 3 1
0.294 0.405 0.240 n.0 0.472 1.418"
0.300 0.438 0.236 0.123 0.466 0.855
½½4
0.756
0.757
~3 ~3 30
0.622* n.0*
0.494 0.186
T~ ~5
0.609*
0.390
mo=1.50+0.15# B
R=8%
*The intensity of these peaks are affected by a large uncertainty because they are superimposed to nuclear peaks. peak intensity is reported in Fig. 6(a) giving an ordering temperature TN = 92 K which is a quite large value for rare earth ternary compounds of ThCr2Si2-type structure. CeRh2Si2 The neutron diffraction diagrams given in Fig. 4(b) show that CeRh2Si2 develops, at low temperature, a magnetic order different from that found in TbRh2Si2. The superlattice magnetic peaks can be indexed by considering the structure to be associated with the wave vector k = [1/2 1/2 0] which corresponds also to a symmetry point of the Brillouin zone. It describes a simple antiferromagnetic ordering within (00 I) planes with a +-+stacking sequence along a [110] direction. The magnetic cell (ax/2, ax/2, c) is actually two times larger than the crystallographic one. The star o f k contains two non-equivalent wave vectors kl = [1/2 1/2 0] and k2 = [1/21/2 0] defining two K-domains. In both of them the magnetic order is the same within a (001) plane, it differs only by the coupling between adjacent (001) planes, i.e. by the coupling between the magnetic moments in (000) and (1/2 1/2 1/2). In the domain kl = [1/2 1/2 0] the coupling is antiferromagnetic (see Fig. 5) while it is ferromagnetic in domain k2 = [1/21/2 0]. Therefore the stacking sequence of (001) planes along the c-axis will not depend on the sign of the exchange interaction I' between nearest neighbouring planes. The best fit (R = 8%) between observed and calculated magnetic intensities (Table 3) indicates that the
689
antiferromagnetic direction is along the c-axis and gives a moment value m0 = 1.50 +- 0.15/aB at T = 10K, close to the free ion value gjJ = 2.14#B. The intensities were calculated by using the form factor given by [10] and the Fermi lengths: bee = 0.482, bRh = 0.591 and bsi = 0.415. The thermal variation of the intensity of the first magnetic peak [1/2 1/2 0], reported in Fig. 6(b), gives an ordering temperature Tlv = 36 K. 4. DISCUSSION The investigation of the magnetic ordering in CeRhzSi2 and TbRh2Si2 provides interesting information about the magnetic anisotropy and the exchange interactions in the RRh2Si z ternary compounds. The large value of the magnetic moment found in TbRh2Si2 indicates that the crystal field, of D4h symmetry, acting on the Tb a+ ions must lead to a ground state with two very close singlets 1/x/r2 06) + I-- 6)) and 1/x/2 0 6 ) - I--6)); then the magnetic moments are quenched along the c-axis giving rise to an Ising4ike behaviour. However, in CeRh2Si: a moment reduction exists which can be explained by a crystal field effect. Actually, a crystal field level scheme similar to that found in CeCu2Si2 [11] with a ground state doublet 10) = 0.9 [+ 5/2) + 0.18 IT-3/2) explains quite well the observed moment value. As far as the magnetic interactions are concerned, they are quite different in both compounds: in CeRh2Si2 the coupling is antiferromagnetic within (001) planes whereas it is ferromagnetic in TbRh2Si2. Actually, a ferromagnetic planar coupling was found in almost all compounds crystallizing with the structure of ThCr2Si2-type [12]. In the ternaries RM2Si2 or RM2G% the M = 3d, 4d or 5d atoms are non-magnetic excepted with Mn [ 13] and the lanthanides or actinides order all with a ferromagnetic coupling in the (001) planes, but the coupling between planes has been found to be ferromagnetic (k = 0), antiferromagnetic (k = [100]), commensurate (k = [001/2]) or incommensurate (k = [00 kz]) [12]. The only exception is TbNi2Si2 [14] in which the in-plane coupling was found to be antiferromagnetic as in CeRh2Si2. Using a molecular field approximation, a simple analysis of the possible magnetic structures can be done in the structure of ThCr2Si~-type because magnetic ions are located in a single body-centered tetragonal Bravais lattice. An antiferromagnetic structure being defined by a wave vector corresponding to a symmetry point of the Brillouin zone (k = H/2) [2], the body-centered tetragonal Bravais lattice with c > a, allows, in addition to the ferromagnetic order (k = 0), only three types of antiferromagnetic structures: AFI with k = [001], AFII with k = [1/2 1/2 0] and AFIII with k = [1/2 0 1/2].
690
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si 2
By considering the in-plane interactions (11, 12 . . . . ) as stronger than the inter-plane ones (I', I " , . . . ) , the ordering within a (001) plane can be only ferro or antiferromagnetic if only two exchange integrals I1 and 12 are taken into account. Actually, three exchange integrals are needed to get an incommensurate or a commensurate order within a (001) plane. The order will be ferromagnetic (k = 0) or antiferromagnetic (k = [1/2 1/2 0]) according to la > 0 or I1 < 0, at least ifI2 has not too large a negative value; in that case (1121> Ill 1/2), the wave vector will be k = [1/2 0 0]. Actually the coupling between planes of RKKY-type is not weak, an estimation can be done easily, when the in-plane coupling is ferromagnetic, by comparing the values of Tar and 0p. For TbRh2Si 2 we get Tar = 92 K and 0p = 43 K indicating that the inter-plane coupling (0p -- Tar) is antiferromagnetic and of the same order of magnitude than the in-plane ferromagnetic coupling. Then, in the case of large inter-plane couplings, incommensurate structures can be stabilized in addition to the antiferromagnetic ones. It must be pointed out that the in-plane component of the wave vector will depend on both the in-plane (11,12) and inter-plane (I', I") exchange integrals. Up to now only the incommensurate structure with a wave vector k = [00kz] has been found in PrCo2Ge2, UPd2Si2 and UPd2Ge2, and a commensurate structure with k = [001/2] exists in UCu2Ge2 [12]. Coming back to the RRh2Si2 compounds, susceptibility measurements [2] have shown that they exhibit at low temperatures an antiferromagnetic order probably with a ferromagnetic in-plane coupling as, for all of them, 0p has a large positive value like in TbRh2Si2, in particular in NdRh2Si 2 the following values 0p = 27 K and Tar = 57 K [2] have been measured. The only exception in the series would be CeRh2Si 2 where 0p has an unusually large negative value (0p = - 61 K), but in comparison a rather small value of the ordering temperature (Tar = 36 K). The explanation of this unexpected result is only due to a change of sign of the first nearest neighbour exchange integral 11 which has a positive value for normal rare earths and a negative value in the case of cerium. Actually, the ferromagnetic (k = 0) and the antiferromagnetic coupling with k = [1/2 1/2 0] are dual by changing the sign of Iv Moreover in this antiferromagnetic structure, imposed by the in-plane exchange integrals 11 and 12, the nearest neighbouring exchange integral between (001) planes (1') is not involved to determine the stacking sequence of (001) planes while it has a large value. Actually, in CeRh2Si2 as in TbRh2Si2, f has a large negative value which explains the important difference between the values of Tar and 0p. Then the large negative value of 0p in CeRh2Si2 is the consequence that the main interactions are all antiferromagnetic (11 < 0, 1~ < 0 and I' < 0). A large negative value of 0p has been
Vol. 49, No. 7
found also in CePd2Si2 (0p = -- 75 K), CeAu2Si2 (0p = 12 K) and CeAg2Si2 (0p = -- 15 K) [15] while these compounds order antiferromagnetically below 10 K. Therefore, these cerium compounds may develop a magnetic order similar to that found in CeRh2Si2, at least in CePd2Si2. In normal rare earth ternary compounds the magnetic coupling is of the RKKY-type and it is quite important in the RRh2Si 2 series probably due to a high density of states at the Fermi energy. However, the sudden change of the sign o f l l in CeRh2Si 2 indicates that the interactions are not only of the RKKY-type in this compound, in particular the usual intra-atomic 4f-5d exchange interaction is not the dominant mechanism. Actually, the dominant exchange interaction in CeRh2Si 2 would be due to the large mixing between 4f and conduction electrons leading to a Kondo-like behaviour. Such a mixing process gives rise to anisotropic indirect interactions in which one part behave as R KKY ones [ 16] but the other part is always antiferromagnetic and decreases exponentially with the distance [17]. This latter contribution could explain the change of sign of I1. A more extensive study of the magnetic properties of CeRh2Si 2 and similar compounds as CePd2Si 2 would be interesting to confirm this idea. -
-
REFERENCES 1.
W. Rieger & E. Parth6, Mh. Chem. 100, 444 (1969). 2. B. Chevalier, P. Lejay, J. Etourneau & P. Hagenmuller, Mat. Res. Bull. 18, 315 (1983), and unpublished results. 3. F. Steglich, J. Aarts, C.B. Bredl, W. Lieke, D. Meschede, W. Franz & H. Schiifer, Phys. Rev. Lett. 43, 1892 (1979). 4. E.R. Bauminger, D. Froindlich, I. Nowik, S. Ofer, I. Felner & I. Mayer, Phys. Rev. Lett. 30, 1053 (1973). 5. R. Batlestracci, C.R. Acad. ScL 282,291 (1976). 6. B. Bressel, B. Chevalier, J. Etourneau & P. Hagenmuller, J. Cryst. Growth 47,429 (1979). 7. C. Godart, L.C. Gupta & M.F. Ravet-Krill, J. Less Common Metals 94, 187 (1983). 8. E. Roudaut,Proc. Workshop on Position-Sensitive Detection of Thermal Neutron, ILL-Grenoble (1982), to be published by Academic Press. 9. J. Rossat-Mignod, Systematics and the Properties of the Lanthanides (Edited by S.P. Sinha) p. 255. (1982). 10. A.J. Freeman & J.P. Desclaux, J. Magn. Magn. Mat. 12, 11 (1979). 11. S. Horn, E. Holland-Moritz, M. Lovenhaupt, F. Steglish, H. Scheuer, A. Benoit & J. Flouquet, Phys rev. B23, 3171 (1981). 12. J. Leciejewics, Proc. IVInt. Conf. on Crystal Electn'c Field and Structural Effects in f-ElectronSystems (Edited by R. Guertin, W. Suski & Z. Zolnierek), p. 279 Academic Press, New York (1982).
Vol. 49, No. 7 13. 14. 15.
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
A. Szytula & S. Siek, J. Magn Magn Mat. 27, 49 (1982). V.N. Nguyen, F. Tch6ou, J. Rossat-Mignod & R. Ballestracci, Solid State Commun. 45,209 (1983). V. Murgai, S. Raaen, L.C. Gupta & R.D. Parks, Valence Instabilities (Edited by P. Wachter & H. Boppart) p. 537. (1982).
16.
17.
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R. Siemann & B.R. Cooper, Phys. Rev. Lett. 44, 1015 (1980); B.R. Cooper and R. Siemann, Crystalline Electric FieM and Structural Effects in f-Electron Systems (Edited by I.E. Crow, R.P. Guertin & T.W. Mikalisin) p. 241. Plenum Press (1980). C. Proetto & A. Lopez, Phys. Rev. B24, 3031 (1981).
Solid State Communications, Vol. 49, No. 7, pp. 685-691, 1984. Printed in Great Britain. MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2 S. Quezel, J. Rossat-Mignod
Laboratoire de Diffraction Neutronique, D6partement de Recherche Fondamentale, Centre d'Etudes Nucl6aires, 85X-38041 Grenoble C6dex, France and B. Chevalier, P. Lejay, J. Etourneau Laboratoire de Chimie du Solide du CNRS, Universit6 de Bordeaux I, 351, cours de la Lib6ration - 33405 Talence C6dex, France
(Received 28 October 1983 by E. F. Bertaut) Magnetic measurements and a neutron diffraction study have been carried out on the ternary compounds TbRh2Si2 and CeRh2Si2 with a tetragonal structure of ThCr2Si2-type. TbRh2Si2 is found to order antiferromagnetically below TN = 92 K with moments along the e-axis. The structure, of wave vector k = [001 ], consists of a stacking of ferromagnetic (001) planes with a + -- + - - sequence. CeRh2Si2 develops below TN = 36 K a structure described by a wave vector k = [1/2 1/2 0] in which the coupling within a (001) plane is antiferromagnetic. This change of coupling together with the large negative value of0p = - 61 K has been attributed to a change of the sign of the first nearest neighbour in-plane interaction which would correspond to an exchange mechanism different from the usual RKKY one in CeRh2Si2. 1. INTRODUCTION THE TERNARY SILICIDES RM2Si2 in which R is a rare earth metal and M is a 3d, 4d or 5d transition element have been extensively studied during the past years. They crystallize in a simple structure of ThCr2Si~type which is tetragonal of space group I4/mmm [1 ]. These ternary silicides allow us to study many interesting physical properties as the supraconductivity, the valence fluctuations, the Kondo effect or the magnetism [2-4]. The magnetic properties of the silieides with a 3d transition element (Mn, Fe, Co, Ni, Cu) have been studied in more detail than those with a noble metal as M = Ru, Rh, Ir. In a recent work we have shown that the RRh2Si 2 (R = Ce, Nd, Sm, Gd, Tb, Dy, Ho, Er) exhibit at low temperatures an antiferromagnetic ordering [2]. In this paper we report the results of a more detailed study on the CeRh2Si2 and TbRh2Si2 silicides by means of neutron diffraction and magnetic measurements.
1.1. Sample preparation CeRh2Si2 and TbRh2Si2 have been prepared by the direct melting of the elements in an arc furnace under a purified argon atmosphere. The obtained compounds were analyzed by X-rays using a Guinier camera and proved to have the quadratic structure of ThCr2Si2type. The lattice parameters at room temperature of
CeRh:Si2 (a = 4.075 A, c = 10.13 A) and of TbRh2Si2 (a = 4.031 A, c = 9.96 A) are in good agreement with the previously published values [5]. In the case of TbRh2Si2 a single crystal (3 mm diameter and 2 mm height) has been grown by using a Czochralski method developed at the University of Bordeaux [6]. 2. MAGNETIC MEASUREMENTS The magnetic measurements have been performed between 4.2 K and 300 K by using a balance of Faraday type and a magnetometer with a vibrating sample. CeRh2Si2 orders antiferromagnetically at TN = 36 K. The magnetic susceptibility follows a Curie-Weiss law (Fig. 1). The effective moment value/ae~ ~ = 2.56/a B is in agreement with cerium in a trivalent state. The paramagnetic Curie temperature 0p = --61 K has a large negative value. These values differ significantly from the quite recent measurements of Godart et al. (0p = -- 72 K, ~ten = 2.9/aB) [7]. TbRh2Si2 orders also antiferromagnetically at TN = 94K. The effective moment value/aen = 10.0/l n is slightly larger than the free ion value of a Tb 3+ ion (/aen = 9.72/~B) which may indicate a positive polarization of the conduction electrons. The paramagnetic Curie temperature 0p = 43 K has a positive value, as in most of the other RRh2Si2 ternaries [2], indicating that 685
686
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
Tb Rh2 Si 2
/
/
4O0
A f\
,,,
/
#
-
c
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/ E
Vol. 49, No. 7
H " 18 kC~
.,,,r
;/ 7
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~
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u'~
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TN
-- 3 6 K
100
I
I
200
300
TEMPERATURE
I
i
L
i
1
I00 200 TEMPERATURE {K)
300
Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility of CeRh2Si2.
(K)
Fig. 3. Temperature dependence of the magnetization of a TbRh2Si2 single crystal measured with a magnetic field of 18 kOe applied along and perpendicularly to the c-axis. the interactions have mainly a ferromagnetic character in TbRh2Si2 (Fig. 2). The magnetization measured on a single crystal, exhibits a large anisotropy depending on the magnetic field is applied along or perpendicularly to the c-axis (Fig. 3). The antiferromagnetic direction is along the c-axis. 3. NEUTRON RESULTS
/ 20
Tb Rh2Si 2
Neutron experiments have been carried out at the Siloe reactor of the CEN-Grenoble. The diffraction patterns were recorded with a linear multidetector spectrometer [8] using a neutron wavelength of 2.483 A. The scattering by the nucleus gives rise to nuclear Bragg peaks which can be well accounted by the extinction condition (h + k + l = 2n + 1) of the body centered-tetragonal space group I4/mmm. The crystal structure of ThCr2Si2-type contains:
/
/ / ¢ E
1,5 O
E "7 E X
P
one R atom in the site 2a: (000) of D4h symmetry; two Rh atoms in the site 4d: (0½¼) and (½0¼); two Si atoms in the site 4e: (00z) and (00~).
J o O
0.19
W s
/
(z:
/
017 I
/ /
8o
/
T KI
/,
,60
'
260
I'EMPERAIURE {K)
Fig. 2. Temperature dependence of the reciprocal magnetic susceptibility of TbRh2Si2.
Then the structure can be described as a stacking of atomic planes perpendicular to the c-axis with the sequence R - S i - R h - S i - R and located respectively at z = 0, 1/2 --Zsi = 0.125, 1/4, Zsi = 0.375 and 1/2. The fit of the calculated and integrated intensities gives no evidence for any mixing between Rh and Si atoms in 4d and 4e sites. As an example a comparison between observed and calculated intensities of a few nuclear peaks are given in Table 1 in the case of TbRh2Si2. A quite good agreement (R = 2.7%) is obtained for Zsi = 0.375, the intensities were calculated using
Vol. 49, No. 7
MAGNETIC ORDERING IN TbRh2Siz AND CeRh=Si2
Tb Rh2Si 2
687
[po]
§ ~o i.
8
"~ L 6
T=15K
t
L) 10 Z
!
;:".'.:;2f;i>~t~:;
c:.~.q=:,'.':'."~$~i=~:~='...:,......,~.:<:~
z
[o02]
~Io]0o3]I~% ~ 2~lai~.o:
n,"
I--6 IM 7
T=IOaK
Ill
,'
4
1
I
5
CeRhaSi
10
I
i
I
[
I
15 20 2,5 30 BRAGG ANGLE(e)
35
I
40
[00,~] 012]
2
[20o]
0o3]
[~14]
L
L 75 °~
.IQ
T= 106 K
roo2]
[.lol]
RhSl
[20
RhSi~
L 50
z
25
0
/
T=IOK
z ~~-
'
'o ~'~
,01"J T:IOK_IO6K ZWo~
............~..,.,~,.,.,..,,,~.~
..:.,........ ~-,............., ..................~ .............::.,~,.,.~, .....................:..[ ....... ~,.~
,,-
i
[~,t1] ,-,-~
~ ~
~'3
[{{o]~ [½,}:z]
,
,
,
5
10
15
,
,
20
25
.,.,..,.~ ~,...
l, ........ , 30
35
[{½s]B½,]I v ............... ,
I
40
BRAGG ANGLE (0) Fig. 4. (a) Neutron diffraction patterns from paramagnetic (103 K) and ordered (15 K) TURh2Si~. Magnetic reflections are associated with a wave vector k = [001 ]. (b) Neutron diffraction patterns from paramagnetic (106 K) and ordered (10 K) CeRh2Si2. Magnetic reflections are associated with a wave vector k = [1/2 1/2 0]. the following scattering lengths: ban, = 0.756, bah = 0.591, bsi = 0.415 x 10-12 cm. As far as the magnetic properties are concerned this structure is quite simple because the magnetic ions (rare earth) are located in one Bravais lattice.
TbRhaSi2 In the neutron diffraction diagrams given in Fig. 4 additional reflections can be identified at T = 15 K. These new reflections, due to the onset of the magnetic order, can be easily indexed on the basis of the
688
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2 C e Rh 2 5i
TbRh25i 2 k'=[O01]
2
2o z
Vol. 49, No. 7
__Ft0j r
J
i
I
I
I
I
I
I
d
I
[
15
U 10
Z
5
o Fig. 5. Magnetic structures of TbRh2Si2 (k = [001 ]) and CeRh2Si2 (k~ = [1/2 1/2 0]). Table 1. Calculated and observed intensities o f the nuclear peaks in barn per TbRh2Si2 molecule at T 15 K (a = 4.027 A, c = 9.952 A, Zsi = 0.375)
2'o 3'o
4b
I
50
I
I
6o 7'0 80
9o loo
TENPERATURE(K)
A2sI
[
I
I
=
h k li
lobs
Ieal
002 10 1 1 10 1 03
0.17 0.14 0.89 13.98
0.36 0.22 0.65 13.98
004 11 t
31.58
31.19
200
26.67
29.05
20
14.58
13.34
~, 151-
R = 2.7%
ce h2s2
_z
z 0
I
I
I
10
20
30
40
TEMPERATURE(K)
Table 2. Calculated and observed intensities o f the magnetic superlattice peaks o f TbRh2Si2 in barn/Tb atom at T = 15K. hk l
lob s
001 1 00 003 1 02 111 1 13 1 04 005 20 1
n.0 17.2 n.0 18.7 29.5 12.4 6.0 n.0 22.1 mo=8.5-+0.3/aB
I~ 0 17.8 0 18.6 26.5 13.1 6.1 0 19.7 R=6.5%
crystallographic unit cell with the following rule h + k + l = 2n 4- I. The magnetic scattering vectors h being defined by the relation h = H + k, whre H spanned the different Brillouin zone centers i.e. the nuclear
Fig. 6. (a) Temperature dependence of the magnetic intensity of the [100] reflection of TbRh2Si 2. (b) Temperature dependence of the integrated intensity of the [1/2 1/2 0] magnetic reflection of CeRh2Si2. lattice vectors, the ordering is described by the wave vector k = [001 ]. This wave vector corresponds to a symmetry point of the Brillouin zone (for c > a) i.e. it describes a truly antiferromagnetic structure [9]. The structure consists of a stacking of ferromagnetic (001) planes with a + - - + - - sequence along the c-axis (Fig. 5). The absence of the [001 ], [0 03] magnetic peaks indicates without any ambiguity that the moments are aligned along the e-axis. The observed intensities (Table 2) can be well accounted (R = 6.7%) by using the Tb 3÷ form factor given by [10]. A moment value mo = 8.5 -+ 0.3/a n is found at T = 15 K indicating that the terbium magnetic moment is close to the free ion value ( g J = 9/an). Moreover there is no evidence of any magnetic moment on the rhodium atoms. The temperature dependence of the [100] magnetic
Vol. 49, No. 7
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
Table 3 Calculated and observed intensities of the magnetic superlattice peaks of CeRh~Si2 in barn/Ce atom at T = 10 K. Magnetic peaks are indexed in the domain associated with k~ = [1/2 1/2 0]. h kl
Iobs
Ieaa
~½0 "I" I ~ 1 ½½2 ½½3 ~0 ~1 3 1
0.294 0.405 0.240 n.0 0.472 1.418"
0.300 0.438 0.236 0.123 0.466 0.855
½½4
0.756
0.757
~3 ~3 30
0.622* n.0*
0.494 0.186
T~ ~5
0.609*
0.390
mo=1.50+0.15# B
R=8%
*The intensity of these peaks are affected by a large uncertainty because they are superimposed to nuclear peaks. peak intensity is reported in Fig. 6(a) giving an ordering temperature TN = 92 K which is a quite large value for rare earth ternary compounds of ThCr2Si2-type structure. CeRh2Si2 The neutron diffraction diagrams given in Fig. 4(b) show that CeRh2Si2 develops, at low temperature, a magnetic order different from that found in TbRh2Si2. The superlattice magnetic peaks can be indexed by considering the structure to be associated with the wave vector k = [1/2 1/2 0] which corresponds also to a symmetry point of the Brillouin zone. It describes a simple antiferromagnetic ordering within (00 I) planes with a +-+stacking sequence along a [110] direction. The magnetic cell (ax/2, ax/2, c) is actually two times larger than the crystallographic one. The star o f k contains two non-equivalent wave vectors kl = [1/2 1/2 0] and k2 = [1/21/2 0] defining two K-domains. In both of them the magnetic order is the same within a (001) plane, it differs only by the coupling between adjacent (001) planes, i.e. by the coupling between the magnetic moments in (000) and (1/2 1/2 1/2). In the domain kl = [1/2 1/2 0] the coupling is antiferromagnetic (see Fig. 5) while it is ferromagnetic in domain k2 = [1/21/2 0]. Therefore the stacking sequence of (001) planes along the c-axis will not depend on the sign of the exchange interaction I' between nearest neighbouring planes. The best fit (R = 8%) between observed and calculated magnetic intensities (Table 3) indicates that the
689
antiferromagnetic direction is along the c-axis and gives a moment value m0 = 1.50 +- 0.15/aB at T = 10K, close to the free ion value gjJ = 2.14#B. The intensities were calculated by using the form factor given by [10] and the Fermi lengths: bee = 0.482, bRh = 0.591 and bsi = 0.415. The thermal variation of the intensity of the first magnetic peak [1/2 1/2 0], reported in Fig. 6(b), gives an ordering temperature Tlv = 36 K. 4. DISCUSSION The investigation of the magnetic ordering in CeRhzSi2 and TbRh2Si2 provides interesting information about the magnetic anisotropy and the exchange interactions in the RRh2Si z ternary compounds. The large value of the magnetic moment found in TbRh2Si2 indicates that the crystal field, of D4h symmetry, acting on the Tb a+ ions must lead to a ground state with two very close singlets 1/x/r2 06) + I-- 6)) and 1/x/2 0 6 ) - I--6)); then the magnetic moments are quenched along the c-axis giving rise to an Ising4ike behaviour. However, in CeRh2Si: a moment reduction exists which can be explained by a crystal field effect. Actually, a crystal field level scheme similar to that found in CeCu2Si2 [11] with a ground state doublet 10) = 0.9 [+ 5/2) + 0.18 IT-3/2) explains quite well the observed moment value. As far as the magnetic interactions are concerned, they are quite different in both compounds: in CeRh2Si2 the coupling is antiferromagnetic within (001) planes whereas it is ferromagnetic in TbRh2Si2. Actually, a ferromagnetic planar coupling was found in almost all compounds crystallizing with the structure of ThCr2Si2-type [12]. In the ternaries RM2Si2 or RM2G% the M = 3d, 4d or 5d atoms are non-magnetic excepted with Mn [ 13] and the lanthanides or actinides order all with a ferromagnetic coupling in the (001) planes, but the coupling between planes has been found to be ferromagnetic (k = 0), antiferromagnetic (k = [100]), commensurate (k = [001/2]) or incommensurate (k = [00 kz]) [12]. The only exception is TbNi2Si2 [14] in which the in-plane coupling was found to be antiferromagnetic as in CeRh2Si2. Using a molecular field approximation, a simple analysis of the possible magnetic structures can be done in the structure of ThCr2Si~-type because magnetic ions are located in a single body-centered tetragonal Bravais lattice. An antiferromagnetic structure being defined by a wave vector corresponding to a symmetry point of the Brillouin zone (k = H/2) [2], the body-centered tetragonal Bravais lattice with c > a, allows, in addition to the ferromagnetic order (k = 0), only three types of antiferromagnetic structures: AFI with k = [001], AFII with k = [1/2 1/2 0] and AFIII with k = [1/2 0 1/2].
690
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si 2
By considering the in-plane interactions (11, 12 . . . . ) as stronger than the inter-plane ones (I', I " , . . . ) , the ordering within a (001) plane can be only ferro or antiferromagnetic if only two exchange integrals I1 and 12 are taken into account. Actually, three exchange integrals are needed to get an incommensurate or a commensurate order within a (001) plane. The order will be ferromagnetic (k = 0) or antiferromagnetic (k = [1/2 1/2 0]) according to la > 0 or I1 < 0, at least ifI2 has not too large a negative value; in that case (1121> Ill 1/2), the wave vector will be k = [1/2 0 0]. Actually the coupling between planes of RKKY-type is not weak, an estimation can be done easily, when the in-plane coupling is ferromagnetic, by comparing the values of Tar and 0p. For TbRh2Si 2 we get Tar = 92 K and 0p = 43 K indicating that the inter-plane coupling (0p -- Tar) is antiferromagnetic and of the same order of magnitude than the in-plane ferromagnetic coupling. Then, in the case of large inter-plane couplings, incommensurate structures can be stabilized in addition to the antiferromagnetic ones. It must be pointed out that the in-plane component of the wave vector will depend on both the in-plane (11,12) and inter-plane (I', I") exchange integrals. Up to now only the incommensurate structure with a wave vector k = [00kz] has been found in PrCo2Ge2, UPd2Si2 and UPd2Ge2, and a commensurate structure with k = [001/2] exists in UCu2Ge2 [12]. Coming back to the RRh2Si2 compounds, susceptibility measurements [2] have shown that they exhibit at low temperatures an antiferromagnetic order probably with a ferromagnetic in-plane coupling as, for all of them, 0p has a large positive value like in TbRh2Si2, in particular in NdRh2Si 2 the following values 0p = 27 K and Tar = 57 K [2] have been measured. The only exception in the series would be CeRh2Si 2 where 0p has an unusually large negative value (0p = - 61 K), but in comparison a rather small value of the ordering temperature (Tar = 36 K). The explanation of this unexpected result is only due to a change of sign of the first nearest neighbour exchange integral 11 which has a positive value for normal rare earths and a negative value in the case of cerium. Actually, the ferromagnetic (k = 0) and the antiferromagnetic coupling with k = [1/2 1/2 0] are dual by changing the sign of Iv Moreover in this antiferromagnetic structure, imposed by the in-plane exchange integrals 11 and 12, the nearest neighbouring exchange integral between (001) planes (1') is not involved to determine the stacking sequence of (001) planes while it has a large value. Actually, in CeRh2Si2 as in TbRh2Si2, f has a large negative value which explains the important difference between the values of Tar and 0p. Then the large negative value of 0p in CeRh2Si2 is the consequence that the main interactions are all antiferromagnetic (11 < 0, 1~ < 0 and I' < 0). A large negative value of 0p has been
Vol. 49, No. 7
found also in CePd2Si2 (0p = -- 75 K), CeAu2Si2 (0p = 12 K) and CeAg2Si2 (0p = -- 15 K) [15] while these compounds order antiferromagnetically below 10 K. Therefore, these cerium compounds may develop a magnetic order similar to that found in CeRh2Si2, at least in CePd2Si2. In normal rare earth ternary compounds the magnetic coupling is of the RKKY-type and it is quite important in the RRh2Si 2 series probably due to a high density of states at the Fermi energy. However, the sudden change of the sign o f l l in CeRh2Si 2 indicates that the interactions are not only of the RKKY-type in this compound, in particular the usual intra-atomic 4f-5d exchange interaction is not the dominant mechanism. Actually, the dominant exchange interaction in CeRh2Si 2 would be due to the large mixing between 4f and conduction electrons leading to a Kondo-like behaviour. Such a mixing process gives rise to anisotropic indirect interactions in which one part behave as R KKY ones [ 16] but the other part is always antiferromagnetic and decreases exponentially with the distance [17]. This latter contribution could explain the change of sign of I1. A more extensive study of the magnetic properties of CeRh2Si 2 and similar compounds as CePd2Si 2 would be interesting to confirm this idea. -
-
REFERENCES 1.
W. Rieger & E. Parth6, Mh. Chem. 100, 444 (1969). 2. B. Chevalier, P. Lejay, J. Etourneau & P. Hagenmuller, Mat. Res. Bull. 18, 315 (1983), and unpublished results. 3. F. Steglich, J. Aarts, C.B. Bredl, W. Lieke, D. Meschede, W. Franz & H. Schiifer, Phys. Rev. Lett. 43, 1892 (1979). 4. E.R. Bauminger, D. Froindlich, I. Nowik, S. Ofer, I. Felner & I. Mayer, Phys. Rev. Lett. 30, 1053 (1973). 5. R. Batlestracci, C.R. Acad. ScL 282,291 (1976). 6. B. Bressel, B. Chevalier, J. Etourneau & P. Hagenmuller, J. Cryst. Growth 47,429 (1979). 7. C. Godart, L.C. Gupta & M.F. Ravet-Krill, J. Less Common Metals 94, 187 (1983). 8. E. Roudaut,Proc. Workshop on Position-Sensitive Detection of Thermal Neutron, ILL-Grenoble (1982), to be published by Academic Press. 9. J. Rossat-Mignod, Systematics and the Properties of the Lanthanides (Edited by S.P. Sinha) p. 255. (1982). 10. A.J. Freeman & J.P. Desclaux, J. Magn. Magn. Mat. 12, 11 (1979). 11. S. Horn, E. Holland-Moritz, M. Lovenhaupt, F. Steglish, H. Scheuer, A. Benoit & J. Flouquet, Phys rev. B23, 3171 (1981). 12. J. Leciejewics, Proc. IVInt. Conf. on Crystal Electn'c Field and Structural Effects in f-ElectronSystems (Edited by R. Guertin, W. Suski & Z. Zolnierek), p. 279 Academic Press, New York (1982).
Vol. 49, No. 7 13. 14. 15.
MAGNETIC ORDERING IN TbRh2Si2 AND CeRh2Si2
A. Szytula & S. Siek, J. Magn Magn Mat. 27, 49 (1982). V.N. Nguyen, F. Tch6ou, J. Rossat-Mignod & R. Ballestracci, Solid State Commun. 45,209 (1983). V. Murgai, S. Raaen, L.C. Gupta & R.D. Parks, Valence Instabilities (Edited by P. Wachter & H. Boppart) p. 537. (1982).
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R. Siemann & B.R. Cooper, Phys. Rev. Lett. 44, 1015 (1980); B.R. Cooper and R. Siemann, Crystalline Electric FieM and Structural Effects in f-Electron Systems (Edited by I.E. Crow, R.P. Guertin & T.W. Mikalisin) p. 241. Plenum Press (1980). C. Proetto & A. Lopez, Phys. Rev. B24, 3031 (1981).